[SOLVED] Elliptic functions

Consider the function where the integral is along any rectifiable path from to . Clearly this is not a single-valued function of , as the value of the integral will depend on the winding number of the path around . Thus is defined up to an integral multiple of . Now consider the inverse function ; we have and therefore is a periodic function. (It's the exponential!)

Now consider the function . Now is defined up to where . Explain why, mimicking the construction of the inverse function as above, we do not obtain an elliptic function.